Well, that was absolutely bizarre. The strace showed errors opening /etc/hsots, but on another machine that works it didn't. The permissions and owners/groups for /etc/hosts were identical and I used the same account to do the ping from on each machine. Adding world +r to the broken machine's host file fixed the problem.

This machine is really afflicted, after this current project (2 weeks until the end), I am probably going to nuke and repave it. At the very least that will get Network Manager up and going again.

I do wish another distribution was an option.

Thanks for the tips.